module 8

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Module 8: Multiferroic and Magnetoelectric Ceramics Introduction

A ferroic material is basically a material which exhibits either ferroelectric or ferromagnetic orferroelastic ordering, a feature typically demonstrated by the presence of a well defined hysteresisloop when the material is switched electrically, magnetically or mechanically. More recently there hasbeen another ordering mechanism proposed which is called as ferrotoroidic ordering. Magnetoelectriccoupling in the materials, on the other hand, is a more general phenomenon irrespective of the stateof magnetic and electrical ordering. For example, it could occur in paraelectric ferromagneticmaterials or it can be mediated by other parameter such as strain.

Hence, the term multiferroic would mean a material exhibiting two or more of the above orderingmechanisms. More recently, multiferroic materials have become of tremendous interests because ofpotential device applications. For example, one can have multi-state memory element or sensorswhich can be operated in multi-mode or spintronic devices. However, there are challenges in finding amaterial that would act as a perfect multiferroic. Most multiferroic materials are not naturally occurringand are made in the laboratory .There are problems with respect to their fabricability, while theirtransition temperatures are often impractical. Despite these challenges, research is on to find amaterial which would emerge as a potential device material. In this module we discuss some of thebasic aspects of multiferroics and a few multiferroic materials.

The Module contains:

Introduction

Historical Perspective

Requirements of a Magnetoelectric and Multiferroic Material

Magnetoelectric Coupling

Type I Multiferroics

Type II Multiferroics

Two Phase Materials

Summary

Suggested Reading:

N. A. Hill, J. Phys. Chem. B, 104, 6694-6709 (2000)

M. Fiebig, J. Phys. D: Appl. Phys., 38, R123–R152 (2005)

W. Eerenstein, N. D. Mathur and J. F. Scott, Nature, 442, 759 (2006)

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Module 8: Multiferroic and Magnetoelectric Ceramics Ferroic Material

8.1 Ferroic Material

Multiferroics are materials which possess more than one type of primary ferroic ordering in a single phase. The general features are

Ferroics are materials like ferroelectrics, ferromagnetic or ferroelastics which exhibit a largechange in the properties of the materials across a critical temperature and show acharacteristic hysteresis loop with two equivalent response states at zero value of stimuli.

The critical temperature, in general, is also accompanied with a symmetry breaking.

Typically known orderings are ferroelectric (coupling of charge polarization and electric field),ferromagnetic (coupling of magnetic moment and magnetic field) and ferroelastic (coupling ofstress and strain) ordering. Another proposed ordering mechanism is ferrotordoicity whichexhibit arrangement of magnetic vortices in an ordered manner, called tordoization.

Figure 8.1 explains the various possible scenarios. While there are a large number ofmagnetically and electrically polarizable materials, there are only a few materials which showferroelectric and ferromagnetic ordering. Magnetoelectric materials are those materials whichare simultaneously electrically and magnetically polarizable, while Multiferroics are strictly thosematerials which show ferroelectric and ferromagnetic ordering.

Figure 8.1 Classification of multiferroic and magnetoelectricmaterials

While, strictly speaking multiferroism means only for those materials in which there is coupling ofmore than one order parameter, now a days, researchers have also started includingantiferromagnetism as well as ferrimagnetism also with multiferroic materials.

The multiferroic materials are either rare earth manganites or ferrites or transition metal perovskiteoxides. The examples are TbMnO3, TbMn2O5, HoMn2O5, LuFe2O4, BiFeO3, BiMnO3 and

YMnO3. Some non-oxides are also multiferroics such as BaNiF4 and spinel chalcogenides, e.g.

ZnCr2Se4.

Given that the multiferroic materials show more than one ferroic ordering, the envisagedapplications are numerous. Some of these applications can be future memory devices with multipledegree of control, sensors and actuators that be controlled by more than one type of stimuli,spintronic devices where spin of electron can be controlled electrically.

Recent reports also classify the multiferroics into Type I and Type II multiferroics. Type I

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multiferroics are those materials in which the source of ferroelectricity and magnetism is differentand the effects are fairly independent of each other, albeit with a small degree of coupling. Incontrast, type II materials are those where magnetism causes the existence of ferroelectricityattributed to the strong coupling between two states. However, the magnitude of polarization is

these materials remains very small, typically less than 10-2 µC/cm2.

There are no text books yet on Multiferroics, however there are a few good reviews1,2,3,4 in theinternational journals which can be referred for an elaborate reading. These reviews have also beensource of much of the basic information in this module.

1N. A. Hill, J. Phys. Chem. B, 104, 6694-6709 (2000)

2M. Fiebig, J. Phys. D: Appl. Phys., 38, R123–R152 (2005)

3W. Eerenstein, N. D. Mathur and J. F. Scott, Nature, 442, 759(2006)

4D. Khomskii, Physics, 2, 20 (2009)

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Module 8: Multiferroic and Magnetoelectric Ceramics Historical Perspective

8.2 Historical Perspective

Magnetoelectric effect was first observed by Rontgen in 1888 and by Pierre Curie in 1894 in twoindependent studies. Rontgen found that a dielectric when moved in an electric field, becamemagnetized and conversely it became polarized when moved in a magnetic field. In contrast, Curiepointed out the magnetoelectric effect based on symmetry considerations. The term magnetoelectricwas first used by Debye in 1926.

The first material with magneto-electric switching was Cr2O3 with small magnitudes of induced

polarization and magnetization. Subsequently the research was carried on various materials and it isnow established that more than 80 compounds including Ti2O3, GaFeO3, boracites, phosphates

showed magnetoelectric effect.

The first ever discovered multiferroic material that was simultaneously ferroelectric and ferromagnetic,was nickel iodine boracite, Ni3B7O13I. Subsequently many studies were made on various boracite

compounds. However, most of them had quite complex crystal structures and materials were notvery useful from technological viewpoint.

This was followed by studies on mixed perovskites, essentially solid solutions of two perovskite oxidecompounds. Russian scientists took the lead in these investigations where they replaced some of the

d0 type cations in the ferroelectric perovskite oxides with magnetic dn type elements in order toinduce magnetic ordering. One of first such compounds to be discovered was a solid solution of Pb(Fe2/3W1/3)O3 and Pb (Mg1/2W1/2)O3. In this compound, ferroelectricity was caused by

diamagnetic Mg and W atoms while magnetic ordering is caused by Fe3+ ions. Some othercandidates were lead based Fe or Co doped tungstates or tantalates which showed ferroelectricityand antiferromagnetic ordering. However, most of these materials had either very low Curietemperatures or Neel temperature which prevented further research on these.

Subsequently, the research focus was on other perovskite materials which are either manganites orferrites and have been more promising than previously research materials and will be discussed laterin this module.

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Module 8: Multiferroic and Magnetoelectric Ceramics Requirements of a Magnetoelectric and Multiferroic Material

8.3 Requirements of a Magnetoelectric and Multiferroic Material

There are many material requirements which need to be fulfilled for a material to be called asmultiferroic. For instance, for ferroelectricity, a material must be non-centrosymmetric to possessspontaneous electrical polarization and there are only a limited number of point groups (out of 32)which allow an unique polar direction. Similarly, spontaneous magnetic moment is permitted by 31point groups. Out of these, 13 point groups allow occurrence of both the properties simultaneously.Since this is not a small number; it is probably unlikely that symmetry plays an important role indetermining a multiferroic.

Electrically, while a ferroelectric material must be an insulator, it is not a constraint for aferromagnetic material. For most ferromagnets, electronically speaking, the conductivity is due tohigh density of states at the Fermi level while the same is not true for ferroelectrics and insulators.However, there are a few magnetic oxides, such as half metallic magnets and ferrimagnetic oxideswhich show reasonable spontaneous magnetism while simultaneously being semiconducting orinsulating.

As far as the chemistry of the material is concerned, most ferroelectrics require ions whose shells

are filled and in case of perovskites the B-atom at the centre of BO6 octahedra must have d0 type

electron configuration. In contrast, magnetic systems require d-orbitals to be partially occupied formagnetic ordering to develop. Latter also puts constraints to maintaining the center of symmetry inthese systems.

Among type I multiferroics, multiple mechanisms of ferroelectricity have been proposed5. For

example, in mixed perovskites, it has been suggested that d0 ions being ferroelectrically active shiftfrom the center of O6 octaehdra while magnetic order is maintained by dn ions. In contrast, in

materials like BiFeO3, ferroelectricity is believed to arise due to the ordering of lone pairs of Bi in one

direction such as [111]. Another proposed mechanism for ferroelectricity is charge ordering i.e. ifafter charge ordering has occurred, the sites have different charges and bonds turn out to be ofunequal lengths. This is seen in materials like TbMn2O5. Finally, materials like YMnO3 exhibit

geometric ordering due to tilting of rigid MnO5 polyhedra, resulting in Y and O atoms coming closer

to each other forming dipoles.

Another factor that could be analyzed is the size of small cation, especially in the perspective ofperovskites. However, upon comparison, one finds that this is not a valid argument as sizes varyconsiderably for different kinds of compounds.

Another contrast between ferroelectric and ferromagnetically ordered systems is that the waystructure is distorted. While ferroelectrics undergo a phase transition as temperature changes, lowtemperature phase being non-centrosymmetric, ferromagnetic materials show significant Jahn-Tellerdistortion arising from partially filled d-shells. The latter is almost absent in most ferroelectrics as ithas been postulated that Jahn-Teller distorted structure may have less driving force for off-centerdisplacement of B-ions in the octahedra.

Another condition which ferroelectric materials show is that they possess a time reversal symmetrybut do not exhibit a space inversion symmetry (i.e. polarization reverses in space). On the other

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hand, ferromagnetic materials possess space inversion symmetry but do not exhibit time inversionsymmetry.

So, in summary, while there is no constraint on various material parameters which prevent materialsfrom being multiferroic i.e. simultaneously ferroelectric and ferromagnetic, a multiferroic does notpossess either time reversal or space inversion symmetry.

5D. Khomskii, Physics, 2, 20 (2009)

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Module 8: Multiferroic and Magnetoelectric Ceramics Magnetoelectric Coupling

8.4 Magnetoelectric Coupling

Landau theory describes the magnetoelectric effect in a single phase material through expansion ofthe free energy expression as

(8.1)

where E and H are the electric and magnetic field respectively. Here e and µ are the dielectricpermittivity and magnetic permeability respectively. The second and the third term in Equation (8.1)

are the temperature dependent electrical polarization, Pis, and magnetization, Mi

s. Fourth and fifth

terms describe the effect of electrical and magnetic field on the electrical and magnetic behaviorrespectively, while sixth term consisting of aij describes linear magnetoelectric coupling. The next two

terms consisting of ßijk and γijk are third rank tensors and represent higher order coupling

coefficients.

Differentiation of Equation (8.1) with respect to electric and magnetic fields respectively leads topolarization and magnetization which are as follows:

and

(8.2)

In most cases, we are interested to know about the linear magnetoelectric coefficient, aij, as

magnetoelectric effect is linear in most compounds. This coefficient basically quantifies thedependence of polarization on magnetic field or of magnetization on the electric field. In case ofmultiferroics, although many linear magnetoelectric effects are expected because these materialsoften possess large susceptibility and permeability respectively, this is not a necessary condition assome ferroelectrics and ferromagnets do show small dielectric susceptibility and magneticpermeability.

In addition to direct coupling, there may be instances of indirect coupling mediated by strain. This islikely to arise in two phase systems where two components are couple via strain. However, morerecently, in cubic SrMnO3 and EuTiO3, strain mediated ME effect is observed in single phase.

Indirect measurements of magnetoelectric coupling include measurement of changes in themagnetization near the magnetic transition temperatures or changes in dielectric constant near themagnetic transition temperature. However, such measurements do not provide any mechanisticinsight into the coupling constant. Direct measurements measure magnetic response of material to anapplied electric field or electric response to an applied magnetic field.

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Module 8: Multiferroic and Magnetoelectric Ceramics

Type I Multiferroics

8.5 Type I Multiferroics

There are a few type I single phase multiferroics. As mentioned earlier, Type I multiferroics are thematerials which have different sources of ferroelectricity and magnetism with the two effects beingquite independent of each other. However, a small degree of coupling cannot be ruled out.

In this section, we will mainly have a look at most studied compounds:

Bismuth Ferrite (BiFeO3)

Bismuth Manganite (BiMnO3) and

Hexagonal Manganites

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Module 8: Multiferroic and Magnetoelectric Ceramics Type I Multiferroics

8.5.1 Bismuth Ferrite (BiFeO3)

One of the most studies multiferroic is Bimusth ferrite or BiFeO3 (BFO), primarily because it has very

high ferroelectric transition temperature (TC = 1100 K)6 and shows G-type antiferromagnetism with

cycloidal spin structure with Neel temperature (TN) of ~ 650 K.7

In its ferroelectric state, as shown in Figure 8.2, BFO possesses a rhombohedrally distorted ABO3

type perovskite structure with space group R3c having lattice parameters, ar = 3.965 Å and = 89.4°

at room temperature.8 Above the Curie temperature, the structure changes to a high symmetry cubicphase.

Figure 8.2 Schematic diagram of the crystal structure ofBiFeO3

The material has been shown to be ferroelectric at room temperature in both single crystal and thin

film form high remanent polarization, more than 50 µC/cm2. 9,10 However, polycrystalline thin films

can be leaky depending upon the methods of preparation and other conditions.11 On the other hand,while magnetic character of pure phase in single crystal form is antiferromagnetic, there have been a

few controversies on magnetism in thin films. Often, impurities like Fe2+ and other iron borne

impurities as well as deoxygenation can result in significant magnetism.12 The material is also proneto containing defects as well as difference valencies of Fe which can alter the material properties.

The periodic spin spiral results in zero magnetic moment and hence linear magnetoelectric effectsaverage to approximately zero. However, properties of BiFeO3 can also be altered by making chemical

substitutions. For example substitution of A-site cation (Bi) by ions such as Ba or Nd13 gives rise tosignificant magnetism in the compound while substitution of B-site cation (Fe) by elements such as

Zr14 results in alteration in the defect chemistry as well as change in the leakage characteristics ofthe material. These effects are attributed to the breaking of spin spiral upon doping. Similarly, epitaxialconstraints can also result in this breaking of spin spirals.

6R. Teague, R. Gerson, and W. J. James, Solid State Commun. 8, 1073 (1970)

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7P. Fischer, M. Polomska, I. Sosnowska, and M. Szymanski, J. Phys. C 13, 1931 (1980)

8G Catalan and J.F. Scott, Advanced Materials, 21, 2463 (2009).

9D. Lebeugle, D. Colson, A. Forget, M. Viret, P. Bonville, J. F. Marucco, and S. Fusil, Phys. Rev. B76, 024116 (2007).

10J. Wang, J. B. Neaton, H. Zheng, V. Nagarajan, S. B. Ogale, B. Liu, D. Viehland, V.Vaithyanathan, D. G. Schlom, U. V. Waghmare, N. A. Spaldin, K. M. Rabe, M. Wuttig, and R.Ramesh, Science 299, 1719 (2003)

11A. Z. Simoes, A. H. M. Gonzalez, L. S. Cavalcante, C. S. Riccardi, E. Longo, and J. A. Varela, J.Appl. Phys. 101, 074108 (2007).

12H. Bea, M. Bibes, A. Barthelemy, K. Bouzehouane, E. Jacquet, A. Khodan, J. P. Contour, S.Fusil, F. Wyczisk, A. Forget, D. Lebeugle, D. Colson and M. Viret, Applied Physics Letters 87 (7),072508 (2005).

13V. A. Khomchenko, D. A. Kiselev, M. Kopcewicz, M. Maglione, V. V. Shvartsman, P. Borisov, W.Kleemann, A. M. L. Lopes, Y. G. Pogorelov, J. P. Araujo, R. M. Rubinger, N. A. Sobolev, J. M.Vieira, and A. L. Kholkin, J. Magn. Magn. Mater. 321, 1692 (2009).

14S. Mukherjee, R. Gupta, A. Garg, V. Bansal, and S. Bhargava, J. Appl. Phys. 107, 123535(2010)

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8.5.2 Bismuth Manganite (BiMnO3)

Bismuth manganite is an interesting multiferroic material with a perovskite structure. It is a lowtemperature ferromagnet and a room temperature ferroelectric. The material shows ferromagnetic

ordering below 105 K attributed to the orbital ordering of B-site ions i.e. Mn3+ ions and a

magnetization of 3.6 µB per formula unit.15 The material has a perovskite triclinic structure which

changes to monoclinic structure at ~450 K and then to a non-ferroelectric orthorhombic phase at

~770K.16 However, the trouble with this material for device application has been its low resistivity,especially in polycrystalline form. The bulk form of material has been shown to exhibit multiferroic

behavior near 80 K17 and negative magneto-capacitance effect in the vicinity of magnetic transition

temperature (Tm) with -0.6% change in the dielectric constant near Tm.16 The problem which arises

with this material is that it requires high pressures in bulk form17. In contrast, recent work has shown

that it can made resistive in thin film form which can be prepared with much ease.18

15H. Chiba, T. Atou, and Y. Syono, Journal of Solid State Chemistry, Volume 132, 139-143 (1997)

16T. Kimura, S. Kawamoto, I. Yamada, M. Azuma, M. Takano, and Y. Tokura, Physical Review B,Volume 67, 180401(R) (2003)

17A. Moreira dos Santos, S. Parashar, A. R. Raju, Y. S. Zhao, A. K. Cheetham, C. N. R. Rao, SolidState Communications, 122, 49-52 (2002)

18W. Eerenstein, F. D. Morrison, J. F. Scott, and N. D. Mathur, Appl. Phys. Lett. 87, 101906 (2005)

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8.5.3 Hexagonal Manganites (TbMnO3, YMnO3)

Hexagonal manganites are another interesting class of manganites and are depicted by the generalformula RMnO3 where R is typically a rare earth ion such as Y and Ho. These materials simultaneously

exhibit ferroelectricity and antiferromagentic ordering of magnetic Mn ions. In general, rare earth

elements having smaller ionic radii, tend to stabilize hexagonal phase of manganites, RMnO319 (R =

Sc, Y, Ho, Er, Tm, Yb, Lu) with space group P63 cm.20 In spite of having a chemical formula, ABO3,

similar to the perovskites, hexagonal manganites have altogether different crystal and electronic

structure. In contrast to the conventional perovskites, hexagonal manganites have their Mn3+ ions with5-fold coordination, located at the center of an MnO5 trigonal bi-prism. R ions, on the other hand, have

7-fold coordination unlike the cubic coordination in perovskites. The MnO5 bi-prisms are two

dimensionally arranged in space and are separated by a layer of R3+ ions. Figure 8.3 shows aschematic representation of YMnO3 unit cell showing ionic arrangements within the structure.

Figure 8.3 Crystal structure of hexagonalYMnO3.21

Crystal field level scheme of Mn3+ ions in hexagonal RMnO3 is also different from that of Mn3+ ions

with octahedral coordination. Here, the d- levels are split into two doublets and an upper singlet. As a

result, four d-electrons of Mn3+ occupy two lowest lying doublets and unlike Mn3+ ion in octahedral

coordination, there is no degeneracy present. Consequently, Mn3+ ions in these compounds are not

Jahn-Teller ions.22

Hexagonal RMnO3 are found to possess considerably high ferroelectric transition temperature (> 500 K).

However, their Neel temperature is far below the room temperature. Table 1 lists the ferroelectric andmagnetic transition temperatures, spontaneous polarization (PS) and effective paramagnetic moment

µeff of some common RMnO3 along with their structural parameters.

The mechanism of ferroelectricity in these compounds also differs from that of the conventional

perovskite oxides. In case of YMnO3, it was observed that off-centering of Mn3+ ion from the center of

22

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the MnO5 biprism is very small and cannot be considered to contribute toward ferroelectricity.

Apparently it turns out that R ions (Y, here) contributes most toward ferroelectricity by having large R-Odipole moments. However, in reality, ferroelectricity in these materials has different origin and can beconsidered as accidental by-product. Similar to BO6 octahedra in perovskite oxides (ABO3), MnO5

trigonal biprism in RMnO3, tilts and rotates in order to ensure closest packed structure. Such tilting of

MnO5 trigonal biprism results in loss of inversion symmetry in the structure and brings about

ferroelectricity.22 Since the mechanisms of ferroelectric and magnetic ordering in the above materials

are quite different in nature, giant effect of magnetoelectric coupling is understandably not present.22

Table 8.1 Lattice parameters, Neel temperature (TN) and ferroelectric Curie(TC) temperature, effective paramagnetic moment (µeff) and spontaneous

polarization (Ps) of some common hexagonal manganites.23,24,25

Compound a(Å) c(Å) TN(K) TC(K) µeff (inµB)

PS

(µC.cm-2)

ScMnO3 5.833 11.17 129 - - -

YMnO3 6.139 11.39 80 920 89 5.5

HoMnO3 6.142 11.42 76 873 11.1 5.6

ErMnO3 6.112 11.40 80 833 10.5 -

TmMnO3 6.092 11.37 86 >573 8.6 0.1

YbMnO3 6.062 11.36 87 993 6.4 5.5

LuMnO3 6.042 11.37 96 >750 5.2 7.5

19S. Lee, A. Pirogov, M. Kang, et al., Nature 451, 805 (2008)

20H. L. Yakel, W. C. Koehler, E. F. Bertaut, et al., Acta. Crystallogr. 16, 957 (1963)

21M. Zaghrioui, V. Ta Phuoc, R. A. Souza, et al., Physical Review B 78, 184305 (2008)

22D. I. Khomskii, Journal of Magnetism and Magnetic Materials 306, 1 (2006)

23J. G. Park, 1st APCTP Workshop on Multiferroics (2008)

24K. Uusi-Esko, J. Malm, N. Imamura, et al., Materials Chemistry and Physics 112, 1029 (2008)

25L. J. Wang, S. M. Feng, J. L. Zhu, et al., Applied Physics Letters 91, 172502 (2007)

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Module 8: Multiferroic and Magnetoelectric Ceramics Type II Multiferroics

8.6 Type II Multiferroics

This class of multiferroics is of the materials which show ferroelectricity in their magnetically orderedstate and that too of a particular type. Moreover, very strong coupling between ferroelectric and

magnetic order parameters has also been observed. In 2003, Kimura et al. reported26 presence ofspontaneous polarization in the magnetized state of the TbMnO3. TbMnO3 has various magnetic

structures: it is an incommensurate antiferromagnet between 27 and 42 K and is commensurateantiferromagnet between 7 and 27 K. It is in the commensurate state between 7 and 27 K, thematerial show ferroelectricity. This discovery was followed by observation of similar effect in TbMn2O5

by Hur et al.27 Subsequently variety of other materials have also been investigated such as Ni3V2O8,

MnWO6 showing this effect. Magnetic spin structure can be either a spiraling cycloid type or a

collinear type.

26T. Kimura1, T. Goto, H. Shintani, K. Ishizaka, T. Arima and Y. Tokura, Nature, 426, p55, (2003)

27N. Hur, S. Park, P. A. Sharma, J. S. Ahn, S. Guha and S-W. Cheong, Nature 429, 392-395(2004)

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Module 8: Multiferroic and Magnetoelectric Ceramics Two Phase Materials

8.7 Two Phase Materials

Another method to for achieving high degree of magnetoelectric coupling is to mix ferroelectric (e.g.BaTiO3) and ferromagnetic (e.g. CoFe2O4) materials and utilize the strain between two phases to

introduce magneto-electric coupling. Such a coupling requires that two phase have good contactbetween them i.e. to have an interface through which properties can coupled such as in the form ofcomposites, epitaxial multilayers and laminates. For a few systems, the data is shown in the tablebelow.

Table 8.2 Magnetoelectric coupling constant data for selected two-phasemagnetoelectric systems

Type of system Materials Couplingconstant(mV/cm-Oe)

Composite28 BaTiO3 and CoFe2O4 50

Laminated composite29 Terfenol-D in polymermatrix and PZT inpolymer matrix

3,000

Laminate30 Terfenol-D/PZT 4,800

Laminate31 La0.7Sr0.3MnO3 and PZT 60

Laminate32 NiFe2O4 and PZT 1,400

Epitaxial thin film

structures33BaTiO3 and CoFe2O4 --

Epitaxial thin film

structures34BiFeO3 and CoFe2O4 --

In two phase structures, as evident from some of references, one can create large changes in themagnetization owing to strain due to the ferroelectric phase transition of the ferroelectric materialduring film growth or one can also attempt to alter the magnetic structure by applying a field thepiezoelectric material which thereby generates a strain in the magnetic material in the vicinity.Epitaxial growth of layers allows very good interfacial contact between two materials as shown in caseof BaTiO3 and CoFe2O4 which has potential to improve the coupling of parameters

28A.M.J.G. van Run, D.R. Terrel, and J.H. Scholing, J. Mater. Sci, 9, p1710-1714 (1974)

29C.-W. Nan et al., Appl. Phys. Lett., 81, 3831–-3833, (2002).

30N. Cai, C.-W. Nan, J. Zhai, and Y. Lin, Appl. Phys. Lett., 84, 3516–-3519 (2004).

31G. Srinivasan, Phys. Rev. B 65, 134402 (2002).

32M.K. Lee et al., Appl. Phys. Lett., 77, 3547–-3549 (2000).

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33H. Zheng et al., Science, 303, 661–-663 (2004).

34F. Zavaliche et al., Nano Lett., 5, 1793–-1796 (2005)

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Module 8: Multiferroic and Magnetoelectric Ceramics

Summary

Summary

Multiferroic and magnetoelectric materials are a new class of materials which show interdependenceof magnetic and electric properties on each other. Moreover, multiferroics simultaneously exhibitferroelectric and magnetic ordering in a single phase with some degree of coupling between orderparameters. While a multiferroic material has to be a single phase material, magnetoelectric materialscan be single phase as well as a mixture of two phases showing interface mediated magnetoelectriccoupling. These materials have the potential for a variety of exciting applications such as dualmemory devices, spintronic devices, high frequency applications etc. However, the applications arerealized yet due to lack of materials and difficulty in achieving the desired effects in the availablematerials. The single phase materials which have been studied well enough in both bulk and thin filmform are BiFeO3, BiMnO3 and hexagonal manganites while two phase mixture studies include

BaTiO3 and CoFe2O4.